IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i12p1938-d1676153.html
   My bibliography  Save this article

The Well-Posedness and Ergodicity of a CIR Equation Driven by Pure Jump Noise

Author

Listed:
  • Xu Liu

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Xingfu Hong

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Fujing Tian

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Chufan Xiao

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Hao Wen

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

Abstract

The current paper is devoted to the dynamical property of the stochastic Cox–Ingersoll–Ross (CIR) model with pure jump noise, which is an extension of the CIR model. Firstly, we characterize the existence and 2-moment of the CIR process with a pure jump process. Consequently, we provide sufficient conditions for the compensated Poisson random measure under which the CIR process with a pure jump process is ergodic. Moreover, the stationary solution can be constructed from the invariant measure. Some numerical simulations are provided to visualize the theoretical results.

Suggested Citation

  • Xu Liu & Xingfu Hong & Fujing Tian & Chufan Xiao & Hao Wen, 2025. "The Well-Posedness and Ergodicity of a CIR Equation Driven by Pure Jump Noise," Mathematics, MDPI, vol. 13(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1938-:d:1676153
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/12/1938/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/12/1938/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1938-:d:1676153. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.